Chapter 7.2, Problem 30PPS

To determine

To find: The pairs of congruent angles and the proportion that relates the corresponding sides.

Answer to Problem 30PPS

The pair of congruent angles is $\angle D\cong \angle K$ , $\angle F\cong \angle M$ and $\angle G\cong \angle J$ and the ratio is $\frac{DF}{KM}=\frac{FG}{MJ}=\frac{GD}{JK}=\frac{5}{4}$ .

Explanation of Solution

Given:

Consider the below diagram.

  

Calculation:

It is given that,

  $\angle F\cong \angle M$ and $\angle G\cong \angle J$ .

Use the Third angles theorem, which shows that $\angle D\cong \angle K$ .

Compare the corresponding sides.

  $\begin{array}{c}\frac{DF}{KM}=\frac{10}{8}\\ =\frac{5}{4}\\ \frac{FG}{MJ}=\frac{5}{4}\\ \frac{GD}{JK}=\frac{\frac{45}{4}}{9}\end{array}$

Solve further as,

  $\frac{GD}{JK}=\frac{5}{4}$

Thus, the pair of congruent angles is $\angle D\cong \angle K$ , $\angle F\cong \angle M$ and $\angle G\cong \angle J$ and the ratio is $\frac{DF}{KM}=\frac{FG}{MJ}=\frac{GD}{JK}=\frac{5}{4}$ .